A common-emitter equivalent circuit is shown in Figure P7.50. (a) What isthe expression for the Miller capacitance? (b) Derive the expression for thevoltage gain A υ ( s ) = V o ( s ) / V i ( s ) in terms of the Miller capacitance andother circuit parameters. (c) What is the expression for the upper 3 dBfrequency? Figure P7.50
A common-emitter equivalent circuit is shown in Figure P7.50. (a) What isthe expression for the Miller capacitance? (b) Derive the expression for thevoltage gain A υ ( s ) = V o ( s ) / V i ( s ) in terms of the Miller capacitance andother circuit parameters. (c) What is the expression for the upper 3 dBfrequency? Figure P7.50
A common-emitter equivalent circuit is shown in Figure P7.50. (a) What isthe expression for the Miller capacitance? (b) Derive the expression for thevoltage gain
A
υ
(
s
)
=
V
o
(
s
)
/
V
i
(
s
)
in terms of the Miller capacitance andother circuit parameters. (c) What is the expression for the upper 3 dBfrequency?
Figure P7.50
(a)
Expert Solution
To determine
The expression for miller capacitance.
Answer to Problem 7.50P
The expression for miller capacitance is,
CM=Cμ(1+gmRL)
Explanation of Solution
Given:
The given circuit is shown below.
Calculation:
Draw the small signal equivalent circuit of figure including the equivalent miller capacitance
From figure, the thevenin voltage across the resistance RB is
VTH=Vi(RBRB+RS)
The equivalent thevenin resistance is,
RTH=RB∥RS
From above figure, the expression for output voltage is,
Vo=−gmVzRL
VoVπ=−gmRL
Av=−gmRL
Determine the expression for the Miller Capacitance.
Av=−gmRL
Determine the expression for the Miller Capacitance.
CM=Cμ(1+|Av|)
Substitute −gmRL for Av in the equation.
CM=Cμ(1+|−gmRL|)
=Cμ(1+gmRL)
Thus, the expression for miller capacitance is,
CM=Cμ(1+gmRL)
(b)
Expert Solution
To determine
The expression for voltage gain.
Answer to Problem 7.50P
The expression for voltage gain
Av(s)=(−βRLrπ+Req)(RBRB+RS)[11+s(rπ∥Req)Ci]
Explanation of Solution
Given:
The given circuit is shown below.
Calculation:
Draw the small signal equivalent circuit of figure including the equivalent miller capacitance
In figure, the capacitors Cx and CM are in parallel.
Ci=Cπ+CM
The value of total capacitive reactance is, 1sCi
Apply voltage division rule to write the expression for voltage Vπ
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